Generating Benders Cuts for a General Class of Integer Programming Problems

This paper proposes a method of generating valid integer Benders cuts for a general class of integer programming problems. A generic valid Benders cut in disjunctive form is presented rst, as a basis for the subsequent derivations of simple valid cuts. Under a qualiication condition, a simple valid Benders cut in linear form can be identiied. A cut generation problem is formulated to elicit it. The simple valid Benders cut is further generalized to a minimally relaxed Benders cut, based on which a complete Benders decomposition algorithm is given, and its nite convergency to optimality is proved. The proposed algorithm provides a way of applying the Benders decomposition strategy to solve integer programs. The computational results show that using the Benders algorithm for integer programs to exploit the problem structures can reduce the solving time more and more as the problem size increases.